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Circular motion in B field
Intermediate
A charge moves in a circle with radius r = mv/qB.
r = mv/qBWith v ⊥ B the force provides centripetal acceleration: qvB = mv²/r, so r = mv/(qB). Faster or heavier particles have larger radii.
A proton at 10⁶ m/s in 1 T: r = 1.04 cm.
The period is independent of speed.
In more detail
A charged particle moving perpendicular to a uniform magnetic field follows a circle of radius r = mv/(qB). Heavier or faster particles have larger circles.
Real-world uses
- Particle detectors measure momentum by the curvature of tracks.
- Cyclotrons use circular motion to accelerate particles.
- Physicists measure the momentum of charged particles from the radius of their circular path in a magnetic field.
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Frequently asked questions
What sets the radius?
The mass, speed, charge and field strength.
Does the particle lose energy?
No. The magnetic force does no work, so the speed and energy stay the same.
Why does a faster particle move in a bigger circle?
Its greater momentum needs a larger radius to keep it turning under the same magnetic force.
Related topics in Magnetism & Induction
Magnetic field lines · Earth's magnetic field · Magnetic force on a moving charge · Cyclotron frequency · Helical motion · Velocity selector